1. Field of the Invention
The present invention relates to an optical correlator and a method for optically correlating. More particularly, the present invention relates to an acousto-optic correlator useful in correlating Doppler sensitive SONAR.
2. Discussion of the Related Art
Undersea reconnaissance is changing along with changes in shipbuilding and propulsion technologies. Active SONAR is taking on new roles, and new signal formats are being investigated. Advances in signal processing have enabled system designers to look beyond Doppler insensitive waveforms in order to take advantage of the additional target discrimination offered by Doppler processing. However, Doppler processing requirements greatly increase the computational load of a SONAR system. Particularly on platforms for which size, weight, and power are critical factors, alternatives to digital signal processing are needed.
Recent technology advances have resulted in a reduction of the sound generated by undersea vehicles. Thus, active techniques for undersea surveillance have taken on new importance. Due to the varied and often turbulent nature of the sea, effective undersea surveillance has become a complex process involving directional projectors, hydrophone arrays, and sophisticated signal processing in order to detect target echoes in the presence of ambient noise and reverberation. One technique to provide echo enhancement over reverberation, which is caused by the reradiation of sound by the sea, is the use of widebeam transmitters and narrowbeam receivers. Thus, large hydrophone arrays are used with either time- or frequency-domain beamforming.
Wideband signals have been employed more recently to provide additional gain over reverberation, with matched filtering or replica correlation being used for signal detection. In order to prevent this detection process from becoming complicated by the Doppler shift induced in echoes from moving targets, Doppler insensitive waveforms such as hyperbolic frequency modulation (HFM) have traditionally been used. Although HFM is Doppler insensitive and acceleration tolerant so that detection under all circumstances (signal-to-noise permitting) is possible, it does not provide the extra target discrimination achievable with Doppler sensitive waveforms.
Most recently, Doppler sensitive waveforms are being reexamined in order to provide this greater target discrimination; however, there is a penalty to be paid--substantially greater computational load in the form of correlation against each of the Doppler shifted replicas.
Correlation and the related process of convolution or matched filtering are primary signal processing techniques used to detect signals in noise, perform synchronization of coded waveforms, or perform pulse compression. Correlation of the two waveforms, s.sub.1 and s.sub.2 may be expressed by the integral: ##EQU1## This integral may be readily performed electronically on two waveforms for a single value of delay, .tau.. In order to perform this correlation simultaneously for many values of .tau., a tapped delay line and parallel mixers and integrators are generally required. Even for this configuration, the number of parallel delays must be limited by the multiplicity of components required. This integral may be performed digitally either directly or through the use of algorithms involving fast Fourier transforms. For digital processing, the processing time and hardware required depend greatly upon the bandwidth and duration of the signals to be processed. Acousto-optic signal processing techniques may be used very effectively and efficiently to perform correlation.
FIG. 1 shows illustrates the diffraction of a laser beam by a conventional acousto-optic Bragg cell 10. The light diffracted from a broad beam of incoming light by a traveling acoustic wave of modulation B(t) moving at velocity v in the z-direction obtains the spatial modulation B(t+z/v) across its wavefront. Since delay .tau. may be related to z/v, both correlation and convolution may be performed by integrating either in time (t) or in space across the wavefront (.tau.) respectively. Correlation may be performed using a convolver and a time-inverted reference, so that correlation may be accomplished using either the time-integrating or space-integrating architectures. For correlation involving signals with time-bandwidth products under 10.sup.4, space integrating architectures are usually most practical.
The basic AO space-integrating convolver 20 is shown in FIG. 2. This is a surface acoustic wave (SAW) implementation in which two Bragg cells 21 and 22 are incorporated onto one substrate. A broad incoming light beam traveling at the Bragg angle 2.theta..sub.B interacts with an acoustic wave S(t) cos (.omega..sub..alpha. t) in Bragg cell 21 which diffracts a portion of that beam. The undiffracted light next interacts with an acoustic wave R(t) cos (.omega..sub..alpha. t) in Bragg cell 22 which also diffracts a portion of that input beam. These diffracted beams have amplitudes proportional to: EQU R(t-z/v) cos (.omega..sub.l +.omega..sub..alpha.)t and EQU S(t+z/v) cos (.omega..sub.l -.omega..sub..alpha.)t
where z is the position along the acoustic wavefront, v is the acoustic velocity, .omega..sub..alpha. is the acoustic frequency and .omega..sub.l is the light frequency. The frequency shifts of these diffracted beams are opposites, since they result from a positive first order diffraction and a negative first order diffraction respectively. The diffracted beams are then focused by a lens 23 to fall on a single wide-area photodetector 24. The resulting photocurrent I will be proportional to the square of the sum of there light amplitudes integrated over the area (space) of the photodetector 24 (hence the name space-integrating convolver). Thus, ##EQU2## The square of the sum contains two square terms, EQU R.sup.2 (t-z/v) cos.sup.2 (.omega..sub.l +.omega..sub..alpha.)t
and EQU S.sup.2 (t+z/v) cos.sup.2 (.omega..sub.l -.omega..sub..alpha.)t,
and a cross-product term, EQU 2R(t-z/v) S(t+z/v) cos (.omega..sub.l +.omega..sub..alpha.)t cos (.omega..sub.l -.omega..sub..alpha.)t.
The cross-product term may be manipulated into frequency sum and difference terms, EQU R(t-z/v) S(t+z/v) cos 2.omega..sub.l t
and EQU R(t-z/v) S(t+z/v) cos 2.omega..sub..alpha. t.
The convolution output is obtained from this frequency difference term. The photodetector 24 cannot respond to the frequency sum term (at twice the light frequency). The square terms result in a DC bias (which may be removed by high pass filtering) and additional terms at twice the light frequency. The convolver output is then: ##EQU3## By a change in variables, this may be written as: ##EQU4## and further as: ##EQU5## which is the more familiar convolution integral in a compressed time frame on an RF carrier.
Additionally, a "doubly diffracted" beam results from the subsequent diffraction of the diffracted beam from Bragg cell 21 by the acoustic wave in Bragg cell 22. This doubly diffracted beam has an amplitude proportional to: EQU R(t-z/v) S(t+z/v) cos (.omega..sub.l +2.omega..sub..alpha.)t
Since the two acoustic waves are at the same carrier frequency, Bragg angles are equal and opposite for the two successive diffractions, so that the doubly diffracted beam is colinear with the undiffracted beam. As with the two first order diffractions, these beams may be focused by a lens 25 onto a large area photodetector 26 with a resulting frequency difference cross product output photodetector current that is proportional to that of the previous case with differences only in scale factor due to differing diffraction efficiencies and in DC bias terms.
In order to use the AO convolver as a replica correlator, it is necessary to input the signal to one Bragg cell and the reference in time-inverted format to the other Bragg cell. In using Doppler sensitive waveforms, the signal must be correlated repeatedly against the reference each time modified for a different degree of Doppler. Since Doppler exhibits itself as a time compression or expansion of the waveform, it is necessary to produce such changes in the reference; if the reference is stored in memory in digital form, it is only necessary to convert the reference from digital to analog (D/A) at a different conversion rate. Since a typical wideband SONAR signal may have a 300 Hz bandwidth at 100-1000 Hz and AO processors require signals in the 10-1000 MHz range, the digital SONAR signals are stored digitally in a buffer memory and read-out through a high speed digital-to-analog converter so that such a signal would be input to the AO convolver at 100 MHz with 30 MHz bandwidth. In this way, signals of several seconds duration are time-compressed (frequency expanded) to signals of 10- 100 .mu.sec and processed in real time allowing over 100,000 different correlations to take place during those several seconds duration. Since the AO convolver operates in real time, a two (2) second signal would be processed in about 40 .mu.sec (to allow signal loading and unloading time in the Bragg cell), and 50,000 correlations may be performed in real time (enough for many beams and Doppler bins).
A one-dimensional AO correlator system was proposed employing the techniques described above with respect to AO convolution. An example of the 1-D AO correlator is shown in FIG. 3 and is designated generally by the reference numeral 30. The structure of 1-D AO correlator 30 is the same as that of AO convolver 20 except that a signal is input to one Bragg cell 21 and the reference signal is input in time-inverted format to the other Bragg cell 22.
Although this 1-D correlator system was shown to be capable of 50,000 correlations in real time, many scenarios are readily developed for which the processing load greatly exceeds this capability. Consider the velocity range of a target to be .+-.75 knots. For a two second SONAR ping at 1000 Hz, the Doppler coverage is (2 v/c)f, where v is the target velocity range, c is the sound velocity, and f is the signal frequency, which is: [(2) (.+-.75 knots)/(3000 knots)] (1000 Hz)=.+-.50 Hz with [1/(2 sec)] or 0.5 Hz resolution creating 200 Doppler bins. With a 1.5 Doppler overlap, 300 bins are required. If the beamformer generates 300 beams, then 300 beams.times.300 Doppler bins=90,000 replica correlations are required. In addition, acceleration producing maneuvers such as turning with a radius of 0.5 miles must be considered. Such a maneuver would span 8 Doppler bins. Thus the number of replica correlations required to include such maneuvers would increase the above figure by a factor of 8, to 720,000 correlations. One may readily show that for this scenario, a digital signal processor would be required to perform of 70.8 .times.10 operations per second.
Since the 1-D correlator 30 was unable to attain this processing rate, 2-D processing must be explored. In radar, narrowband Doppler approximation is made in order to perform 2-D AO correlations with time bandwidth products exceeding 10.sup.6 covering many Doppler bins. This narrowband approximation treats the Doppler shift as a constant frequency shift across the entire signal bandwidth. In SONAR, the velocity of sound in the sea does not permit this. For a wideband signal at frequency f with bandwidth .DELTA.f, the Doppler shift at the lower band edge is: EQU f'=(f-.DELTA.f/2)(2v/c)
and at the upper band edge is: EQU f"=(f+.DELTA.f/2)(2v/c).
The difference between f' and f" is (2 v/c).DELTA.f. Since there must be less than 360.degree. of relative phase shift for the upper end of the signal band with respect to the lower end during the integration interval, the time-bandwidth product limitation may be found by setting: (2 v/c).DELTA.fT&lt;1 where T is the integration interval. Thus the time-bandwidth product .DELTA.fT&lt;(c/2 v). For the current example, a 300 Hz bandwidth with 2 second integration, a 600 time-bandwidth product (TBP), could only be processed over .+-.2.5 knots. Thus, a two-dimensional correlator using the narrowband approximation could only process 10 simultaneous Doppler bins (15 considering overlap). If this were acceptable, a new Doppler modified reference could be used for each .+-.2.5 knot segment of an overall .+-.75 knot target velocity range.